TYPECHECK(x,numeric)
END_TYPECHECK(lgamma(x))
- return lgamma(ex_to_numeric(x));
+ return lgamma(ex_to<numeric>(x));
}
if (!arg_pt.info(info_flags::integer) || arg_pt.info(info_flags::positive))
throw do_taylor(); // caught by function::series()
// if we got here we have to care for a simple pole of tgamma(-m):
- numeric m = -ex_to_numeric(arg_pt);
+ numeric m = -ex_to<numeric>(arg_pt);
ex recur;
- for (numeric p; p<=m; ++p)
+ for (numeric p = 0; p<=m; ++p)
recur += log(arg+p);
return (lgamma(arg+m+_ex1())-recur).series(rel, order, options);
}
TYPECHECK(x,numeric)
END_TYPECHECK(tgamma(x))
- return tgamma(ex_to_numeric(x));
+ return tgamma(ex_to<numeric>(x));
}
{
if (x.info(info_flags::numeric)) {
// trap integer arguments:
- if (x.info(info_flags::integer)) {
+ const numeric two_x = _num2()*ex_to<numeric>(x);
+ if (two_x.is_even()) {
// tgamma(n) -> (n-1)! for postitive n
- if (x.info(info_flags::posint)) {
- return factorial(ex_to_numeric(x).sub(_num1()));
+ if (two_x.is_positive()) {
+ return factorial(ex_to<numeric>(x).sub(_num1()));
} else {
throw (pole_error("tgamma_eval(): simple pole",1));
}
}
// trap half integer arguments:
- if ((x*2).info(info_flags::integer)) {
+ if (two_x.is_integer()) {
// trap positive x==(n+1/2)
// tgamma(n+1/2) -> Pi^(1/2)*(1*3*..*(2*n-1))/(2^n)
- if ((x*_ex2()).info(info_flags::posint)) {
- numeric n = ex_to_numeric(x).sub(_num1_2());
- numeric coefficient = doublefactorial(n.mul(_num2()).sub(_num1()));
- coefficient = coefficient.div(pow(_num2(),n));
- return coefficient * pow(Pi,_ex1_2());
+ if (two_x.is_positive()) {
+ const numeric n = ex_to<numeric>(x).sub(_num1_2());
+ return (doublefactorial(n.mul(_num2()).sub(_num1())).div(pow(_num2(),n))) * pow(Pi,_ex1_2());
} else {
// trap negative x==(-n+1/2)
// tgamma(-n+1/2) -> Pi^(1/2)*(-2)^n/(1*3*..*(2*n-1))
- numeric n = abs(ex_to_numeric(x).sub(_num1_2()));
- numeric coefficient = pow(_num_2(), n);
- coefficient = coefficient.div(doublefactorial(n.mul(_num2()).sub(_num1())));;
- return coefficient*power(Pi,_ex1_2());
+ const numeric n = abs(ex_to<numeric>(x).sub(_num1_2()));
+ return (pow(_num_2(), n).div(doublefactorial(n.mul(_num2()).sub(_num1()))))*power(Pi,_ex1_2());
}
}
// tgamma_evalf should be called here once it becomes available
if (!arg_pt.info(info_flags::integer) || arg_pt.info(info_flags::positive))
throw do_taylor(); // caught by function::series()
// if we got here we have to care for a simple pole at -m:
- numeric m = -ex_to_numeric(arg_pt);
+ const numeric m = -ex_to<numeric>(arg_pt);
ex ser_denom = _ex1();
for (numeric p; p<=m; ++p)
ser_denom *= arg+p;
TYPECHECK(y,numeric)
END_TYPECHECK(beta(x,y))
- return tgamma(ex_to_numeric(x))*tgamma(ex_to_numeric(y))/tgamma(ex_to_numeric(x+y));
+ return tgamma(ex_to<numeric>(x))*tgamma(ex_to<numeric>(y))/tgamma(ex_to<numeric>(x+y));
}
// treat all problematic x and y that may not be passed into tgamma,
// because they would throw there although beta(x,y) is well-defined
// using the formula beta(x,y) == (-1)^y * beta(1-x-y, y)
- numeric nx(ex_to_numeric(x));
- numeric ny(ex_to_numeric(y));
+ const numeric nx = ex_to<numeric>(x);
+ const numeric ny = ex_to<numeric>(y);
if (nx.is_real() && nx.is_integer() &&
ny.is_real() && ny.is_integer()) {
if (nx.is_negative()) {
TYPECHECK(x,numeric)
END_TYPECHECK(psi(x))
- return psi(ex_to_numeric(x));
+ return psi(ex_to<numeric>(x));
}
/** Evaluation of digamma-function psi(x).
static ex psi1_eval(const ex & x)
{
if (x.info(info_flags::numeric)) {
- numeric nx = ex_to_numeric(x);
+ const numeric nx = ex_to<numeric>(x);
if (nx.is_integer()) {
// integer case
if (nx.is_positive()) {
// psi(n) -> 1 + 1/2 +...+ 1/(n-1) - Euler
- numeric rat(0);
- for (numeric i(nx+_num_1()); i.is_positive(); --i)
+ numeric rat = 0;
+ for (numeric i(nx+_num_1()); i>0; --i)
rat += i.inverse();
return rat-Euler;
} else {
// half integer case
if (nx.is_positive()) {
// psi((2m+1)/2) -> 2/(2m+1) + 2/2m +...+ 2/1 - Euler - 2log(2)
- numeric rat(0);
- for (numeric i((nx+_num_1())*_num2()); i.is_positive(); i-=_num2())
- rat += _num2()*i.inverse();
- return rat-Euler-_ex2()*log(_ex2());
+ numeric rat = 0;
+ for (numeric i = (nx+_num_1())*_num2(); i>0; i-=_num2())
+ rat += _num2()*i.inverse();
+ return rat-Euler-_ex2()*log(_ex2());
} else {
// use the recurrence relation
// psi(-m-1/2) == psi(-m-1/2+1) - 1 / (-m-1/2)
// to relate psi(-m-1/2) to psi(1/2):
// psi(-m-1/2) == psi(1/2) + r
// where r == ((-1/2)^(-1) + ... + (-m-1/2)^(-1))
- numeric recur(0);
- for (numeric p(nx); p<0; ++p)
+ numeric recur = 0;
+ for (numeric p = nx; p<0; ++p)
recur -= pow(p, _num_1());
return recur+psi(_ex1_2());
}
if (!arg_pt.info(info_flags::integer) || arg_pt.info(info_flags::positive))
throw do_taylor(); // caught by function::series()
// if we got here we have to care for a simple pole at -m:
- numeric m = -ex_to_numeric(arg_pt);
+ const numeric m = -ex_to<numeric>(arg_pt);
ex recur;
for (numeric p; p<=m; ++p)
recur += power(arg+p,_ex_1());
TYPECHECK(x,numeric)
END_TYPECHECK(psi(n,x))
- return psi(ex_to_numeric(n), ex_to_numeric(x));
+ return psi(ex_to<numeric>(n), ex_to<numeric>(x));
}
/** Evaluation of polygamma-function psi(n,x).
return log(tgamma(x));
if (n.info(info_flags::numeric) && n.info(info_flags::posint) &&
x.info(info_flags::numeric)) {
- numeric nn = ex_to_numeric(n);
- numeric nx = ex_to_numeric(x);
+ const numeric nn = ex_to<numeric>(n);
+ const numeric nx = ex_to<numeric>(x);
if (nx.is_integer()) {
// integer case
if (nx.is_equal(_num1()))
// to relate psi(n,m) to psi(n,1):
// psi(n,m) == psi(n,1) + r
// where r == (-)^n * n! * (1^(-n-1) + ... + (m-1)^(-n-1))
- numeric recur(0);
- for (numeric p(1); p<nx; ++p)
+ numeric recur = 0;
+ for (numeric p = 1; p<nx; ++p)
recur += pow(p, -nn+_num_1());
recur *= factorial(nn)*pow(_num_1(), nn);
return recur+psi(n,_ex1());
// use psi(n,1/2) == (-)^(n+1) * n! * (2^(n+1)-1) * zeta(n+1)
return pow(_num_1(),nn+_num1())*factorial(nn)*(pow(_num2(),nn+_num1()) + _num_1())*zeta(ex(nn+_num1()));
if (nx.is_positive()) {
- numeric m = nx - _num1_2();
+ const numeric m = nx - _num1_2();
// use the multiplication formula
// psi(n,2*m) == (psi(n,m) + psi(n,m+1/2)) / 2^(n+1)
// to revert to positive integer case
// to relate psi(n,-m-1/2) to psi(n,1/2):
// psi(n,-m-1/2) == psi(n,1/2) + r
// where r == (-)^(n+1) * n! * ((-1/2)^(-n-1) + ... + (-m-1/2)^(-n-1))
- numeric recur(0);
- for (numeric p(nx); p<0; ++p)
+ numeric recur = 0;
+ for (numeric p = nx; p<0; ++p)
recur += pow(p, -nn+_num_1());
recur *= factorial(nn)*pow(_num_1(), nn+_num_1());
return recur+psi(n,_ex1_2());
if (!arg_pt.info(info_flags::integer) || arg_pt.info(info_flags::positive))
throw do_taylor(); // caught by function::series()
// if we got here we have to care for a pole of order n+1 at -m:
- numeric m = -ex_to_numeric(arg_pt);
+ const numeric m = -ex_to<numeric>(arg_pt);
ex recur;
for (numeric p; p<=m; ++p)
recur += power(arg+p,-n+_ex_1());
git://www.ginac.de / ginac.git / blobdiff